The invention relates generally to a current-controlled type division circuit.
In FIG. 1, shown is a circuit diagram of a prior art current-controlled type division circuit. In this figure, a pair of transistors Q1 and Q2 constitute a difference circuit in which the emitters of the respective transistors are commonly connected and the commonly connected emitters thereof are connected to a constant source I.sub.E. A dividend signal e.sub.s is applied through a resistor R1 to the base of the transistor Q1. The base of the transistor Q2 is grounded through a resistor R2. The anodes of diodes D1 and D2 are connected to the bases of the transistors Q1 and Q2, respectively, and the cathodes of the diodes D1 and D2 are commonly connected to each other. The collector of a transistor Q3 is connected to the commonly connected cathodes of the diodes D1 and D2. The transistor Q3 has an emitter connected through a resistor R3 to ground and a base to which a division voltage E.sub.B is applied.
In the division circuit thus arranged, the following equation will be established. EQU V.sub.be1 +V.sub.d2 =V.sub.be2 +V.sub.dl ( 1)
where V.sub.be1 and V.sub.be2 represent base-emitter voltages of the transistors Q1 and Q2, respectively, and V.sub.d1 and V.sub.d2 represent anode-cathode voltages of the diodes D1 and D2, respectively.
For each of the transistors and also for each of the diodes, the following equation will be introduced. ##EQU1## where K represents Boltzmann's constant, q an electron density, T an absolute temperature, I.sub.s a backward saturation current and I.sub.e represents an emitter current of the transistor or a forward current of the diode.
Equation (1) can be rewritten as follows. EQU V.sub.be1 +V.sub.d2 -V.sub.be2 -V.sub.d1 =0 (3)
By substituting equation (2) into equation (3), the following will be obtained. ##EQU2##
The following will be obtained by arranging equation (4). ##EQU3##
In equation (5), since the backward saturation currents I.sub.s of the transistors and those of the diodes can be considered to be approximately equal to one another, the following relationship will be established. ##EQU4## Therefore, ##EQU5## Equation (7) can further be rewritten as follows. ##EQU6##
Referring back to FIG. 1, it is now assumed that the resistances of the resistors R1 and R2 are equal to each othr, i.e., R1=R2=R, then the following equations (9) to (11) will be established. ##EQU7##
By substituting equations (9) to (11) into equation (8), the following equation will be obtained. ##EQU8## As apparent from equation (15), the collector current I.sub.cQ2 of the transistor Q2 (which is equal to .alpha. times of the emitter current I.sub.eQ2 thereof) is proportional to the value of e.sub.s /I.sub.B, that is, the signal e.sub.s divided by the sum of the currents flowing in the diodes D1 and D2. It can thus be seen that the division circuit is formed by the provision of the diodes D1 and D2 where the division is effected by the sum of the currents flowing in these diodes with respect to the dividend signal e.sub.s.
However, in the case that the division voltage E.sub.B is inadvertently not applied to the division circuit, the divisor current I.sub.B becomes approximately zero, so that the collector current I.sub.cQ2 flowing into the transistor Q2 becomes infinite as can be understood from equation (15). Thus, it is disadvantageous in the prior art circuit that the gain of the circuit increases abruptly.